'>     ^> 


ANTHROPOLOGY  IIBRARY 

BERKELEY  LIBRARY 


UC-NRLF 


C    E    751    773 


GIFT 
NOV  12  »9IS 


A  SUGGESTIVE  MAYA   INSCRIPTION 


BY 


CHARLES    P.    BOWDITCH 


CAMBRIDGE 
THE  UNIVERSITY   PRESS 

1903 


A  SUGGESTIVE   MAYA    INSCRIPTION 


BY 


CHARLES    P.    BOWDITCH 


CAMBRIDGE 
THE   UNIVERSITY   PRESS 

1903 


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A   SUGGESTIVE   MAYA   INSCRIPTION. 

The  Mayas  had  three  methods  of  marking  a  fixed  date.     The 

first  of  these  was  accomplished  by  stating  the  name  of  one  of  the 

twenty  days  together  with  its  number,  and  declaring  it  to  be  a 

given  day  of  a  given  month.     This  fixed  a  day  exactly  within  the 

limits  of  fifty-two  years.     The  second  method  was  by  stating  that 

between   the   given   day  and   a   date   far   in    the  past,  a   certain 

number  of  days  had  elapsed.     The  date  in  the  past,  from  which 

the  count  was  made,  was  called  4  Ahau  8  Cumhu.     Almost  all 

the  Initial  Series  on   the  monuments  of   Central  America  show 

dates  which  are  over  i,3(X),ooo  days  from  4  Ahau  8  Cumhu.     The 

system  of  numeration  used  by  the  Mayas  to  denote  these  large 

numbers  was   to   a   great   extent  vigesimal,  and    the   periods  so 

used  have  received  the  following  names  from  many  of  the  leading 

Americanists : 

Kin,  I  day. 

Uinal  =20  kins,  20  days. 

Tun     =:i8uinals  =360  kins,  360  days. 

Katun  =  20  tuns     =  360  uinals  =  7,200  kins,  7,200  days. 

Cycle  =  20  katuns  =  400  tuns    =  7,200  uinals  =  144,000  kins,  144,000  days. 

In  the  inscriptions  apparently  13  cycles  are  needed  to  make 
one  of  the  next  higher  term,  while  in  the  manuscripts  20  cycles 
are  used  to  reach  the  next  higher  term.  These  periods  are 
expressed  on  the  inscriptions  either  by  more  or  less  geomet- 
rical forms  or  by  faces,  while  the  numbers  which  tell  the  number 
of  the  periods  are  expressed  by  either  the  line  and  dot  method  or 
by  faces.  In  the  manuscripts  the  terms  of  this  series  are  usually 
shown  simply  by  the  position,  the  higher  terms  being  above  the 
lower  ones.     In  this  article  I  use  the  method  by  position,^  except 

1  I  omit  the  designation  of  the  glyph  called  by  Goodman  the  "  grand  cycle  " 
glyph,  as  I  think  the  evidence  which  we  now  have  tends  to  disprove  this  meaning. 


268724 


2  A   SUGGESTIVE  MAYA   INSCRIPTION. 

that  instead  of  having  the  higher  terms  above  the  lower,  the  higher 
terms  will  be  placed  at  the  left  of  the  lower ;  thus  a  date  given  as 
9.  12.  2.  o.  16.,  means  that  9  cycles  of  I44,cxx)  days,  12  katuns 
of  7,200  days,  2  tuns  of  360  days,  o  uinal,  and  16  kins  have 
passed.  This  is  equal  to  a  total  of  1,383,136  days,  and  counting 
this  from  4  Ahau  8  Cumhu,  there  can  be  but  one  day  reached, 
which  is  5  Cib  14  Yaxkin,  a  date  which  appears  on  two  stelae  of 
Piedras  Negras.  In  stating  a  date  by  this  method  the  Mayas  did 
not  speak  of  a  current  period,  but  of  a  period  elapsed. 

The  third  method  of  fixing  a  given  date  is  by  using  the  first 
method  given  above  and  declaring  that  this  date  is  in  a  given 
katun.  As  this  date  can  only  occur  once  in  fifty-two  years  and  as 
a  katun  extends  over  a  period  of  less  than  twenty  years,  it  is  evi- 
dent that  a  given  date  occurring  in  a  given  katun  cannot  occur 
twice  in  the  same  katun.  Therefore  such  a  day  expressed  as 
belonging  to  a  given  katun  fixes  that  day  with  absolute  certainty 
in  a  term  of  over  seven  hundred  years.  And  more  than  this,  if  the 
date  is  stated  as  occupying  a  particular  position  in  a  given  katun, 
as  for  instance  the  beginning  day  of  a  katun,  such  a  combination 
will  not  occur  again  for  many  thousand  years. 

As  is  well  known  the  inscriptions  on  monuments  and  buildings 
in  Central  America  contain  between  forty  and  fifty  Initial  Series, 
in  which  a  date  is  expressed  by  the  first  and  second  methods  as 
given  above.  In  addition  to  this,  dates  are  often  expressed  in  the 
inscriptions  by  the  first  and  third  methods  given  above,  and  this 
would  be  nearly  as  accurate  a  way  of  fixing  a  date  as  the  combina- 
tion of  the  first  and  second  methods.  The  advantage  of  expressing 
dates  by  the  first  and  second  methods  is  that  if  any  error  should 
occur  in  carving  either  the  day  or  month  glyph  or  the  number 
and  period  glyphs,  one  method  would  tend  to  correct  the  other. 

Whether  Dr.  Seler's  explanation  of  the   meaning  of    this  glyph   is   correct  is  still 
uncertain. 


A  SUGGESTIVE  MAYA   INSCRIPTION.  3 

If  it  were  possible  to  connect  with  certainty  the  date  4  Ahau 
8  Cumhu,  from  which  all  these  other  dates  are  counted,  with  our 
own  chronology,  we  could  easily  reach  a  clear  knowledge  of  the 
dates  on  which  these  monuments  were  erected  and  these  inscrip- 
tions were  carved,  always  provided,  however,  that  the  dates  so 
given  are  records  of  the  dates  of  the  erection  of  the  monuments, 
or  at  least  of  the  buildings  in  which  the  inscriptions  are  found ;  and 
this,  I  think,  is  now  generally  conceded  to  be  the  case  in  almost  all 
instances.  Where  several  dates  are  found  on  the  same  inscription, 
it  will  perhaps  be  safe  to  take  the  latest  one  as  the  date  of  erec- 
tion of  the  monument  or  building.  Although  it  may  not  be 
possible  to  connect  these  dates  with  our  own  chronology,  it  is 
certainly  possible  to  make  use  of  them  to  assign  the  time  when 
these  monuments  were  erected,  and  when  the  cities  which  contain 
them  were  flourishing,  in  relation  to  each  other. 

Omitting  from  consideration  certain  dates,  which  would  seem 
to  be  traditional,  or  merely  samples  of  mathematical  calculations,  I 
give  in  the  following  table  the  earliest  and  latest  dates  of  most  of 
the  cities  of  Central  America  in  which  the  dates  can  be  deciphered 
with  certainty. 

Dates  marked  "  A  "  are  stated  by  combinations  of  the  first  and 
second  methods;  those  marked  "B"  by  a  combination  of  the 
first  and  third  methods : 


Earliest  Date. 

Latest  Date. 

Copan,^ 

A    9.    6.  10.    0. 

0. 

A 

9- 

16.  10.  0. 

0. 

Palenque  {mSr/^es}, 

A    9.    8.    9.  13. 

0. 

B 

9- 

13.      0.  0. 

0. 

Piedras  Negras, 

A    9.    8.  10.    6. 

16. 

B 

9- 

14.    0.  0. 

0. 

Yaxchilan, 

B    9.    8.    8.    4. 

5- 

(?) 

B 

9- 

17.      0.  0. 

0. 

Quirigua, 

A     9.   14.   13.     4. 

17- 

A 

9. 

19.   13.  0. 

.2.(?) 

Seibal, 

B  10.      0.      0.      0. 

0. 

B 

10. 

I.      0.  0. 

0. 

Chichen  Itza  {^&iT}y 

A  10.      2.      9.      I. 

9- 

1  It  is,  of  course,  entirely  possible  that  future  discoveries  will  show  dates  earlier 
and  later  than  those  that  are  given  here,  and  it  may  be,  therefore,  necessary  to  alter 
the  views  which  are  here  expressed,  if  such  discoveries  are  made. 


4  A  SUGGESTIVE  MAYA   INSCRIPTION. 

The  relative  position  of  the  cities  can  be  seen  by  a  glance  at 
a  map.  The  River  Motagua  flows  in  a  northerly  direction  in 
Guatemala  near  the  boundary  between  Guatemala  and  Honduras, 
and  falls  into  the  Caribbean  Sea.  At  an  elevation  of  1700  feet 
above  the  sea  and  not  far  from  the  Motagua  River  and  within 
the  limits  of  Honduras,  Copan  is  situated.  Quirigua  is  in  Guate- 
mala near  its  eastern  boundary  and  close  to  the  Motagua  River 
and  about  twenty-five  miles  from  Copan  as  the  crow  flies. 

The  River  Usumacinta  also  flows  northerly,  but  it  falls  into  the 
Bay  of  Campeche,  a  portion  of  the  Gulf  of  Mexico.  For  a  part 
of  its  course  it  forms  the  boundary  between  Guatemala  and  Mexico. 
Yaxchilan  is  on  the  Mexican  side  of  this  river,  while  Piedras 
Negras  is  farther  down  and  is  in  Guatemala. 

Palenque  is  in  Mexico  on  a  branch  of  the  Usumacinta,  and  is 
much  nearer  the  sea  than  the  other  cities.  Higher  up  a  large 
branch  flows  into  the  Usumacinta  from  the  east;  this  is  called  the 
Rio  de  la  Pasion;  and  on  its  south  bank  and  directly  south  of 
Yucatan  is  Seibal.  This  ruin  is  in  the  northerly  part  of  Guatemala. 
Tikal  is  in  the  very  northeasterly  corner  of  Guatemala,  close  to 
British  Honduras,  and  almost  exactly  south  of  Bacalar  in  Yucatan, 
while  northwest  of  Bacalar  lies  Chichen  Itza.  Tikal  is  about 
seventy  or  eighty  miles  from  Seibal  and  on  the  direct  road  from 
that  place  to  Bacalar,  and  nearly  on  the  direct  road  to  Chichen 
Itza. 

The  traditions  of  the  Mayas  were  that  a  part  of  their  ancestors 
came  from  a  westerly  direction.  Let  us  see  what  possible  migra- 
tions the  dates  which  we  have  found  suggest  to  us.  Wherever 
they  came  from  they  were  apparently  settled  in  Copan  in  9.  6.  10. 
o.  o. ;  in  Palenque  in  9.  8.  9.  13.  o.,  and  in  Piedras  Negras  in  9.  8. 
10.  6.  16.,  and  in  Yaxchilan  in  9.  8.  8.  4.  5.  It  would  seem  as  if  the 
race  had  come  from  the  south  and  west,  and  while  one  branch 
pressed  along  the  mountain  ranges  to  Copan,  another  had  settled  in 


A   SUGGESTIVE  MAYA   INSCRIPTION.  5 

the  Usumacinta  Valley  at  Palenque,  Piedras  Negras,  and  Yaxchilan, 
certain  dates  of  these  three  cities  being  less  than  one  year  apart. 
Copan  extended  itself  along  the  river,  and  somewhere  about  9.  14. 
o.  o.  o.  it  may  have  sent  forth  a  colony  to  Quirigua  or  may  have 
decided  to  form  a  new  settlement  to  which  the  whole  city  might 
move  later.  At  all  events  we  find  no  initial  date  later  than  9.  16. 
10.  o.  o.  in  Copan,  while  Quirigua  flourished  until  nearly  ten  cycles 
had  elapsed. 

The  latest  date  on  the  Usumacinta  River  is  9.  17.  o.  o.  o.,  while 
the  latest  date  of  Quirigua  is  9.  19.  13.  o.  12.,  less  than  seven 
years  before  the  end  of  the  cycle,  and  it  must  have  been  about 
this  time  that  the  emigration  northward  occurred.  Emigrants 
going  from  Quirigua  to  Lake  Ysabal  and  up  the  Rivers  Polochic 
and  Cahabon  would  have  easily  reached  the  head-waters  of  the 
Pasion  on  which  Seibal  is  situated,  while  a  comparatively  short 
land  journey  would  have  enabled  the  inhabitants  of  Piedras  Negras 
and  of  Yaxchilan  to  reach  the  same  place.  From  there  a  short 
journey  would  have  brought  them  to  the  Island  of  Flores  in  Lake 
Peten,  and  another  short  journey  would  have  taken  them  to  Tikal, 
whence  their  march  would  extend  to  Bacalar  and  Chichen  Itza. 
If  this  migration  occurred,  and  if  a  date  were  to  be  found  in  Tikal, 
we  should  expect  it  to  lie  between  10.  o.  o.  o.  o.,  which  is  found 
in  Seibal,  and  10.  2.  9.  i.  9.,  found  in  Chichen  Itza.  In  fact  we 
find  on  a  wooden  carving,  now  in  the  Museum  at  Basel  and  taken 
from  Tikal,  a  date  given  twice  and  reading  3  Ahau  3  Mol,  and 
this  date  is  found  in  10.  o.  15.  8.  o.  It  is  true  that  3  Ahau  3  Mol 
is  also  found  elsewhere,  but  the  same  date,  3  Ahau  3  Mol,  is  fol- 
lowed on  the  second  carving  by  the  glyph  given  in  Fig.  2.  Here 
the  head  is  the  well  known  cycle  glyph,  the  lower  part  of  the  prefix 
is  also  well  known  as  meaning  zero,  while  the  central  part  is  clearly 
15  and  the  upper  part  is  unknown.  This  glyph  may  well  mean 
that   no   katuns   and    15    tuns   are   to   be   counted  in   the   given 


6  A   SUGGESTIVE   MAYA   INSCRIPTION. 

cycle,  and    this   will  fix  the  place  of  3  Ahau   3  Mol  beyond  per- 
adventure.^ 

I  have  attempted  in  my  article  on  the  "  Age  of  the  Maya 
Ruins,"  to  show  the  possibility  of  agreement  between  the  state- 
ments of  the  Books  of  Chilan  Balam  and  the  dates  on  some  of  the 
inscriptions.  Following  in  the  same  line,  we  learn  from  the  Book 
of  Chilan  Balam  of  Mani  that  in  Ahau  6,  the  discovery  of  Ziyan 
caan  or  Bakhalal  took  place.^  This  is  clearly  the  same  as  Bacalar. 
We  learn  also  that  they  ruled  in  Bakhalal  for  about  sixty  years, 
until  Ahau  13,  and  while  they  ruled  there  Chichen  Itza  was  discov- 
ered. At  the  latter  place  they  ruled  for  about  120  years  or  until 
Ahau  I.  It  must  be  remembered  that  the  ahaus,  which,  as  given 
here,  are  the  same  as  katuns,  are  numbered  13.  11.  9.  7.  5.  3.  i.  12. 
10.  8.  6.  4.  2.  13.,  etc. 

The  Book  of  Chilan  Balam  of  Tizimin  relates  that  in  Ahau  8, 
about  twenty  years  before  Ahau  6,  Chichen  Itza  was  "  learned 
about "  and  that  the  **  discovery  of  the  province  of  Zian  took 
place."  This  book  also  states  that  in  Ahau  13  "Pop  was  counted 
in  order,"  and  that  in  Ahau  i  Chichen  Itza  was  destroyed  after  a 
residence  of  120  years  there.  The  Book  of  Chilan  Balam  of 
Chumayel  states  that  in  Ahau  6  Chichen  Itza  was  discovered,  that 
in  Ahau  13  *'  Pop  was  set  in  order,"  and  that  in  Ahau  10  Chichen 
Itza  was  abandoned.  (This  is  forty  years  after  the  date  fixed  by 
the  Book  of  Tizimin.)  In  spite  of  the  discrepancies  in  these 
accounts,  it  seems  clear  enough  that  the  emigrants  reached  Bacalar 
or  Bakhalal  before  they  came  to  Chichen  Itza.  Their  earlier  wan- 
derings are  also  set  forth  in  these  books,  and  while  the  location  of 
Tula,  Chacnouitan,  and  the  earlier  cities  cannot  be  absolutely 
determined,  the  names  of  Bacalar  and  Chichen  Itza  are  well  known. 

1  I  think  that  this  is  a  far  more  probable  date  than  that  suggested  by  Seler  in  his 
valuable  article  on  Tikal  published  in  the  "Zeitschrift  fiir  Ethnologic,"  January, 
1901. 

2  See  "  The  Maya  Chronicles,"  by  Dr.  Daniel  G.  Brinton. 


A   SUGGESTIVE  MAYA   INSCRIPTION.  7 

If,  then,  they  journeyed  from  Seibal  to  Tikal  and  thence  to  Bacalar, 
the  date  of  3  Ahau  3  Mol,  10.  o.  15.  8.  o.,  is  a  probably  accurate 
one. 

Another  proof,  however,  is  found  to  support  this  opinion.  As 
has  been  seen,  the  Books  of  Tizimin  and  Chumayel  state  that 
"  Pop  was  set  in  order  "  about  this  time.  Pop  was  the  first  month 
of  the  year,  and  as  Bishop  Landa  states,  the  year  began  in  his  time 
on  the  i6th  of  July.  It  is  evident  that  if  no  intercalary  days  were 
added  or  if  the  right  number  were  not  added,  the  year  dates  would 
no  longer  agree  with  the  seasons,  and  after  long  wanderings  it 
would  be  very  probable  that  Pop,  or  the  beginning  of  the  year, 
would  need  to  be  "  set  in  order." 

The  method  adopted  by  the  Mayas  for  making  their  dates  corre- 
spond with  the  seasons  is  not  clearly  or  definitely  stated  anywhere. 
Bishop  Landa  says,  **  Tienen  su  afio  perfect©  como  el  nuestro  de 
CCC  y  LXV  dias  y  VI  horas.  .  .  .  Destas  seis  horas  se  hazian 
cada  quatros  anos  un  dia  y  assi  tenian  de  quatro  en  quatro  anos  el 
ano  de  CCCLXVI  dias."  The  manuscripts  do  not  seem  to  show 
this.  Pages  46-50  of  the  Dresden  Codex  would  seem  to  show 
that  for  104  years  no  such  addition  was  made,  unless  it  was  done 
without  giving  a  name,  or  number,  or  a  place  in  the  month  to 
the  intercalated  days.  And  the  count  of  cycles,  katuns,  etc.,  on 
the  inscriptions  is  to  the  same  effect.  It  is  certainly  possible  that 
as  the  count  of  time  was  of  little  importance  to  the  common  peo- 
ple who  received  from  their  priests  and  leaders  their  orders  about 
ceremonies,  planting,  harvesting,  etc.,  the  day  and  month  count, 
and  the  cycle  and  katun  count  were  allowed  to  run  along  without 
change  and  that  the  priests  kept  an  account  of  the  extra  days 
which  had  been  added,  or  would  have  to  be  added,  in  order  to  keep 
their  reckoning  of  days  and  seasons  in  accord.  In  this  case  every 
now  and  then  the  priests  would  have  to  make  these  calculations 
and  find  out  just  where  they  were  in  reference  to  the  seasons. 


8  A  SUGGESTIVE  MAYA   INSCRIPTION. 

Cogolludo,^  Libro  IV,  Capitulo  5,  says,  "  Contaban  los  anos  con 
trescientos  sesenta  y  cinco  dias  divididos  por  meses  de  a  veinte 
dias  correspondiendo  a  los  nuestros.  ...  A  diez  y  siete  de  Julio 
comenzaba  el  mes  llamado  Poop.  .  .  ." 

And  we  find  the  following  statement  made  by  Aguilar,^  in  the 
*'  Anales  del  Museo  Nacional  de  Mexico/'  Tomo  VI,  page  95 : 
"  Contavan  los  anos  por  Lunas  de  365  dias  como  nosotros  tambien. 
Contavan  el  ano  solar  por  meses  de  veinte  dias,  con  seis  dias  de 
Caniculares,  correspondiendo  a  nuestros  meses  por  este  orden  .  .  . 
a  17  de  Julio  Poop.  .  .  .  Esta  quenta  de  diez  y  ocho  meses  y  los 
seis  dias  de  Caniculares  son  los  mismos  365  de  nuestro  afio  solar. 
.  .  .  Assi  ni  mas  ni  menos  usavan,  y  usan  estos  Indios  sus 
refrancillos  in  estos  18  meses,  y  seis  dias  de  Caniculares  para  sem- 
brar  y  mirar  por  su  salud,  y  curarse  como  nosotros  en  Verano, 
Estio,  Otoiio  y  Invierno." 

The  Mexican  system  of  intercalation  is  also  doubtful.  Many 
authors  think  that  the  Mexicans  added  one  day  every  fourth 
year;  others  that  they  added  thirteen  days  at  the  end  of  every 
fifty-two  years,  while  Leon  y  Gama  in  speaking  of  the  intercala- 
tion of  days  every  fifty-two  years  writes,  on  pages  52  and  53  of 
"  Los  Dos  Piedras,"  as  follows :  "  Dije  aquellos  12  6  13  dias,  porque 
efectivamente  un  ano  intercalaban  12,  y  otro  13  dias;  6  lo  que  es 
lo  mismo,  doce  dias  y  medio  en  cada  uno,  6  25  en  el  doble  periodo 
nombrado  Cehuehuetiliztli,  que  constaba  de  104  anos,  como  se 
ha  dicho  antes;  empezando  a  contar  los  dias  intercalares,  en  el 
primer  ciclo,  desde  la  media  noche  .  .  .  de  manera  que  todos 
los  dias  del  primer  ciclo  se  contaban  desde  la  media  noche,  y 
todos  del  segundo  desde  el  medio  dia;  ...  con  lo  qual  quedaban 
intercalados  los  25   dias  en  el  periodo  mayor,  6   doble  ciclo  de 

1  Cogolludo  was  a  priest  of  the  order  of  St.  Francis,  and  took  the  habit  on 
March  31st,  1629. 

2  Aguilar  was  a  native  of  Valladolid  in  Yucatan.  He  studied  in  Mexico,  and  in 
1588  received  a  doctor's  degree  from  the  college  Santa  Maria  de  Todos  Santos. 


A  SUGGESTIVE   MAYA   INSCRIPTION.  9 

104  anos."  Orosco  y  Berra  thinks  that  they  divided  each  260 
years  into  five  sets  of  fifty-two  years  each,  and  that  they  added 
the  intercalary  days  thus:  13,  12,  13,  12,  13.  He  refers  to  the 
Codex  Borgia  for  the  proof  of  this,  but  the  passage  hardly  bears 
out  his  view.     Humboldt  follows  Leon  y  Gama. 

The  Mexican  and  Maya  calendars  were  constructed  on  prac- 
tically the  same  principle,  and  it  is  hardly  possible  that  the 
Mexicans,  who  were  not  as  advanced  as  the  Mayas  in  their 
general  knowledge,  could  have  surpassed  them  in  the  accuracy 
of  their  calculations  of  the  needed  intercalation  of  days.  It  is, 
therefore,  very  probable  that  we  shall  gain  some  knowledge  of 
the  method  used  by  the  Mayas  in  the  use  of  their  days  by  con- 
sidering the  Mexican  method. 

The  inscription  of  Tikal,  ¥\g.  i,^  gives,  in  my  opinion,  some 
evidence  of  the  system  used  by  the  Mayas.  Bear  in  mind  that 
about  this  time  *'  Pop  was  set  in  order."  On  the  inscription  we 
find   Glyphs    i   and  2,  meaning  3  Ahau  3  Mol,  which  we   have 

decided  to  be  the  date 10.  o.  15.    8.    o. 

Glyphs  4  and  5  give  the  distance  for  3  Ahau 

3  Mol  to  6  Eb  o  Pop 2.  II.  12. 

Glyphs  6  and  7  give  6  Eb  o  Pop,^  which  would 

then  be 10.  o.  18.     i.  12. 

10.  o.  18.  I.  12  =  1,446,512  days  =  3963  years  and  17  days. 

3963  years  =  38  x  104  years  +  u  years. 

1  Maudslay,  in  his  "  Biologia  Centrali- Americana,"  shows  the  number  4  attached  to 
the  tun  sign  in  Glyph  5  of  this  inscription,  but  a  reference  to  Plate  12  of  the  "Compte 
rendu  d'une  mission  scientifique  en  Espagne  et  en  Portugal,"  par  Leon  de  Rosny, 
Paris,  1882,  will  show  that  the  number  is  2. 

2  Dr.  Seler  chooses  to  consider  that  the  glyph  before  Pop  means  the  "day 
before,"  but  I  know  of  no  authority  for  this  except  the  unwillingness  of  Dr.  Seler  to 
follow  Mr.  Goodman's  suggestion  that  the  days  of  the  month  were  numbered  from 
o  to  19  —  a  suggestion  which  I  think  is  supported  by  the  facts  in  the  case.  In  other 
words,  I  think  the  evidence  is  very  strong  in  favor  of  the  theory  that  the  Mayas  counted 
the  days  of  their  months  —  not  as  current  days,  but  as  days  elapsed,  as  they  did  their 
cycles,  katuns,  tuns,  uinals,  and  kins,  and  as  we  do  our  hours  and  minutes.  Our 
astronomers  use  o  hours  o  minutes  in  stating  their  observations. 


lO  A  SUGGESTIVE   MAYA   INSCRIPTION. 

If  we  consider  that  the  Mayas  allowed  twenty-five  days  every 
104  years,  as  is  stated  by  Leon  y  Gama  to  be  the  system  of  the 
Mexicans,  and  one  day  for  each  four  years  on  the  shorter  period, 
we  should  find  that  they  would  have  to  allow  for  this  long  period 
38  X  25  +  2  X  I  or  952  days  in  all.  This  is  the  exact  number 
given  on  Glyphs  4  and  5,  where  2.  11.  12.  are  noted. 

Two  methods  are  possible  for  intercalating  these  952  days 
without  disturbing  the  count. 

One  of  these  would  be  to  follow  our  own  method,  by  which 
we  insert  an  extra  day  between  the  28th  of  February  and  the 
1st  of  March,  which  usually  come  together,  and  which  on  leap 
years  are  separated  by  the  29th  of  February.  The  inscription 
seems  to  show  that  this  method  was  known  by  the  Mayas,  for, 
while  Glyphs  6  and  7  give  us  6  Eb  o  Pop,  Glyph  13  is  i  Kin,  the 
kin  sign  being  placed  between  the  open  jaws  made  by  Caban  as 
the  lower  jaw  and  an  unknown  glyph  as  the  upper  jaw,  and  the 
date  7  Ben  i  Pop,  the  next  day  to  6  Eb  o  Pop  appears  on 
Glyphs  14  and  15.  It  is  not  impossible  that  Glyphs  8  to  12  may 
describe  this  method.  This  particular  form  of  i  Kin  occurs  very 
seldom  in  the  manuscripts. 

But  there  was  another  method  of  intercalation  and  this  was 
to  follow  the  Roman  custom.  The  Romans  simply  counted  the 
sixth  of  the  Kalends  of  March  over  again,  calling  the  day  the 
bisextile.  If  then  on  reaching  6  Eb  o  Pop,  the  Mayas  decided 
to  follow  this  plan,  they  would  have  counted  back  952  days  to 
3  Ahau  3  Mol  or,  what  is  the  same  thing,  they  would  have  given 
to  6  Eb  o  Pop  the  name  of  3  Ahau  3  Mol,  and  would  have  begun 
counting  the  days  between  over  again.  When  in  doing  this  they 
had  reached  6  Eb  o  Pop  again,  the  tropical  year  and  the  calendar 
would  have  been  found  to  be  nearly  in  accord. 

It  has  been  suggested,  however,  that  this  may  have  been  done 
simply  as  a  record,  and  that  there  may  have  been  no  attempt  to 


A   SUGGESTIVE   MAYA    INSCRIPTION. 


Fig.  2. 


Fig.  3. 


Fig.  4. 


Fig.  I. 


IFiG.rs- 


12  A  SUGGESTIVE  MAYA  INSCRIPTION. 

carry  out  the  correction  in  a  practical  way ;  but  I  think  it  probable 
that  they  actually  carried  out  this  correction,  and  that  this  record 
of  Tikal  may  be  paraphrased  in  this  way :  **We  have  now  reached 
the  day  6  Eb  o  Pop,  which  should  be  the  beginning  of  the  year 
and  the  sun  should  be  returning  from  its  northward  course,  but 
instead  of  this  it  has  not  reached  the  end  of  its  winter  course 
towards  the  south.  We  should  have  added  25  days  each  104  years 
since  the  beginning  of  time,  or  since  4  Ahau  8  Cumhu,  and  i  day  for 
each  four  years  of  the  remaining  years.  This  would  have  amounted 
to  952  days  and  we  can  add  them  now,  if  we  wish.  If  we  count 
the  next  952  days  without  giving  them  number  or  name,  the 
953d  will  then  be  i  Pop,  but  this  will  be  a  very  cumbersome 
method,  for  how  shall  we  be  able  to  tell  where  we  are  with  so 
many  days  without  name  or  number?  What  we  had  better  do  is 
to  count  back  952  days  to  3  Ahau  3  Mol  and  begin  to  count  these 
days  over  again,  so  that  when  we  reach  6  Eb  o  Pop  again,  we 
shall  find  the  sun  again  coming  back  from  his  northerly  journey." 

As  I  have  said  before,  we  actually  find  the  date  6  Eb  o  Pop, 
the  952  days  which  are  needed  to  be  intercalated,  and  the  date 
3  Ahau  3  Mol  952  days  before  6  Eb  o  Pop,  on  the  Tikal  inscrip- 
tion. The  date  3  Ahau  3  Mol  would  then  be  the  beginning  of 
the  intercalated  days,  which  were  to  be  counted  over.  The  prefix 
to  Pop  is  somewhat  blurred  in  Glyph  7,  and  it  may  be  objected 
that  this  glyph  may  not  mean  o  and  is,  therefore,  not  the  begin- 
ning day;  but  such  an  objection  is  unsound,  for  in  Glyph  13  we 
find  a  glyph  for  i  kin  or  i  day,  and  in  Glyphs  14  and  15  is 
the  date  7  Ben  i  Pop,  just  one  day  in  advance  of  the  last 
one. 

It  is  interesting  also  to  see  that  160  days  before  3  Ahau  3  Mol, 
or  on  the  date  10.  o.  15.  o.  o.,  the  total  number  of  days  equal  to 
1,445,400  had  passed.  This  equals  3960  years  of  365  days  each, 
or  eleven  times  360  years.     It  also  equals  2475  times  584  days. 


A  SUGGESTIVE  MAYA   INSCRIPTrOIV.  1 3 

which  is  almost  exactly  the  time  of  a  synodical  revolution  of 
Venus.  The  date,  then,  must  have  been  a  significant  one  to  the 
Mayas,  since  not  only  an  exact  number  of  years  of  365  days  each 
had  passed,  but  this  number  was  just  eleven  times  360  of  such 
years.  But  an  exact  number  of  Venus  revolutions  had  also 
passed.  It  would  be  wise,  therefore,  to  look  for  a  rectification  of 
the  Venus  revolutions  as  well  as  for  a  rectification  of  the  calendar, 
especially  as  in  Glyph  16  we  find  the  Venus  symbol.  The  fact 
that  the  Mayas  understood  that  a  revolution  of  Venus  was  com- 
pleted in  584  days  needs  no  demonstration  to  a  student  who  has 
carefully  examined  pages  46  to  50  of  the  Dresden  Codex,  where 
the  glyphs  of  Venus,  Figs.  3  and  4,  are  clearly  marked.  But  if 
the  Mayas  had  this  knowledge  and  if  they  had  made  astronomical 
observations  for  a  long  number  of  years,  they  would  naturally  not 
only  have  known  that  the  year  of  365  days  did  not  coincide  with 
the  tropical  year,  but  also  that  the  revolution  of  Venus  was  not 
exactly  584  days.  The  synodical  revolution  of  Venus  is  really 
583.92  days  or  -^^  of  a  day  less  than  584  days.  The  Mayas,  of 
course,  had  no  decimal  system,  and  if  they  made  any  correction 
they  would  be  likely  to  express  it  in  a  fraction  with  i  for  its 
numerator.  As  a  matter  of  fact  ^2  ^^  ^  ^^Y  ^^  ^  ^^^X  close 
approximation  to  -^f^,  and  it  would  be  natural  for  them  to  have 
decided  that  the  correction  should  be  made  at  the  rate  of  one 
day  in  each  twelve  Venus  revolutions.  When  6  Eb  o  Pop  had 
been  reached  there  would  have  passed  1,446,512  days,  or  2476 
revolutions  of  Venus,  and  528  days  additional.  If,  then,  in  the 
correction  of  the  calendar,  they  had  called  6  Eb  o  Pop,  3  Ahau 
3  Mol,  and  had  again  counted  these  days  a  second  time,  when 
they  reached  6  Eb  o  Pop  again,  952  additional  days  would  have 
passed.  This  added  on  to  2476  Venus  revolutions  and  528  days 
would  have  made  2478  revolutions  and  312  days.  If  now  we 
carry  out  the  correction  of  the  Venus  revolution,  by  dividing  the 


14  A  SUGGESTIVE  MAYA  INSCRIPTION. 

number  of  revolutions  by  twelve,  we  should  have  206J  days,  or  say 
207  days,  over  which  the  Venus  revolution  had  progressed  beyond 
the  distance  to  which  the  calculation  of  584  days  to  a  revolution 
had  carried  us.  That  is,  on  reaching  6  Eb  o  Pop  a  second  time, 
2478  revolutions  would  have  passed  and  519  days  of  the  next 
revolution.  This  being  the  case,  we  find  on  the  inscription  in 
Glyph  13  one  day  marked,  and  in  Glyphs  14  and  15  the  date 
7  Ben  I  Pop.  On  this  date,  then,  2478  revolutions  and  520  days 
had  passed.  In  Glyph  16  ¥\g.  5  occurs.  And  here  we  find  as  a 
superfix  the  Venus  symbol,  which  we  have  seen  so  frequently  on 
pages  46  to  50  of  the  Dresden  Codex.  Some  calculation  about 
Venus  is  surely  going  on,  and  when  in  Glyph  17  we  find  the  date 
6  Caban,  and  find  that  this  date  is  just  sixty-four  days  from  7  Ben 
I  Pop,  and  further  find  that  by  adding  this  sixty-four  days  to  the 
520  days  which  had  passed  on  the  additional  revolution  of  Venus 
it  just  completes  this  revolution,  it  would  seem  that  there  can  be 
hardly  any  doubt  that  this  was  intended.  In  other  words,  on  the 
day  6  Caban  given  in  Glyph  17,  2479  Venus  revolutions  were 
exactly  finished. 

It  may  be  objected  that  the  methods  adopted  by  the  Mayas 
for  correcting  their  calendar  and  the  revolutions  of  Venus  are 
not  absolutely  correct,  and  that,  therefore,  any  such  corrections 
would  not  have  brought  about  a  proper  accordance  of  the  calendar 
with  the  seasons  and  with  the  position  of  Venus.  It  is  true  that 
the  methods  are  not  exactly  correct,  but  we  have  here  an  instance 
of  where  two  mistakes  have  actually  rectified  each  other  as  far  as 
the  name  of  the  day  is  concerned.  At  the  time  when  the  date 
6  Eb  o  Pop,  or  10.  o.  18.  i.  12.,  first  appears,  1,446,512  days  had 
passed,  or,  on  the  basis  of  365  days  to  the  year,  3963  years  and  17 
days.  The  number  of  days  to  be  intercalated  under  the  Gregorian 
system  would  have  been  960,  and  if  we  suppose  that  the  Mayas  went 
back  960  days  and  then  counted  these  days  over  a  second  time,  when 


A  SUGGESTIVE  MAYA   INSCRIPTION.  1 5 

they  had  reached  6  Eb  o  Pop  for  the  second  time  the  additional 
960  days  would  have  been  counted  and  the  beginning  of  the  year 
would  have  taken  its  proper  place  with  the  seasons.  At  this  time 
the  number  of  revolutions  of  Venus  which  had  passed  would  be 
2478.55,  the  new  revolution  having  advanced  320  days.  On  the 
basis  that  the  Venus  revolution  actually  consisted  of  583.92  days 
instead  of  584  days,  we  should  find  that  Venus  had  advanced  yj^  of 
a  day  further  for  each  revolution.  This  would  have  amounted  to 
the  sum  of  198.28  days  in  the  number  of  revolutions  just  given. 
Adding  this  number  to  320,  we  have  518.28  days  which  the  new 
revolution  had  passed  through  when  6  Eb  o  Pop  occurred  for  the 
second  time.  The  manuscripts  then  give  one  day  and  then  state 
a  date,  which  is  sixty-four  days  farther  in  advance.  Adding  these 
two  sums  to  518.28  we  get  583.28,  whereas  an  additional  revolu- 
tion of  Venus  would  have  been  583.92,  thus  showing  that  in 
spite  of  the  errors  in  the  calculations  of  the  Mayas,  the  Venus 
revolution  would  have  ended  on  a  day  6  Caban,  the  difference  in 
the  two  calculations  being  less  than  a  single  day. 

The  Tikal  inscription  is,  therefore,  in  my  opinion,  very  strong 
evidence  in  support  of  the  following  views,  viz. : 

1.  That  astronomy  is  one  of  the  subjects  of  which  the  inscrip- 
tions treat. 

2.  That  the  truth  of  the  records  of  Chilan  Balam  is  confirmed 
by  the  inscriptions,  both  in  regard  to  the  correction  of  the  cal- 
endar and  the  migrations  of  the  Maya  races. 

3.  That  the  Mayas  did  correct  their  calendar  shortly  before 
their  arrival  at  Chichen  Itza  and  that  at  the  same  time  they 
corrected  their  observations  of  the  synodical  revolution  of 
Venus. 

4.  That  the  Mayas  intercalated  or  at  least  calculated  the 
intercalation  of  twenty-five  days  each  104  years,  and  allowed  one 
day  for  each  four  years  during  portions  of  those  periods. 


l6  A  SUGGESTIVE  MAYA  INSCRIPTION. 

If  it  should  be  found  that  several  of  the  inscriptions  are  really 
calculations  of  the  corrections  which  are  needed  in  the  calendar 
and  in  the  synodical  revolution  of  Venus,  it  may  throw  some  light 
upon  the  table  on  page  24  of  the  Dresden  Codex,  where  the 
number  2920  (or  8  x  365,  or  5  x  584)  is  the  difference  used,  and 
which,  together  with  many  others  of  similar  tables,  I  have  for  a 
long  time  regarded  as  multiplication  tables,  whatever  they  may 
be  besides.  But  now  we  may  find  that  it  is  also  a  division  table 
in  which  the  division  takes  place  through  subtraction. 

For  instance,  supposing  it  was  desired  to  find  out  how  many 
times  2920,  the  common  multiple  of  365  and  584,  appears  in  the 
date  we  have  been  discussing:  10.  o.  15.  8.  o.,  and  that  we  know 
that  9.  9.  16.  o.  o.  found  in  the  second  column  equals  72  periods 
of  52  years,  or  36  periods  of  104  years,  or  468  times  8  years. 

From  10.    o.  15.    8.  o. 

we  will  deduct  9.    9.  16.    o.  o.  =  468  X  8  years, 

leaving 

Again  deducting  the  number  found 

in  the  centre  row  of  the  page,  4.  17.    6.  o.  =    12X8  years, 

there  is  left 

Again  deducting  4.  17.    6.  o.  =    12x8  years, 

leaving 
Again  deducting  the  number  found 

in  the  fifth  row  of  the  page,  i.    4.    6.  o.  -      3X8  years, 

there  is  left  8.  o. 

We  have  then  a  total  of  495  X  8  years, 

or  of  495  X  5  Venus  revolutions. 

We  find,  then,  that  10.  o.  15.  8.  o.  =  495  x  2920  +  160  days. 
This,  then,  equals  8  X  495  =  3960  solar  years  of  365  days  plus 
160  days,  or  2475  synodical  revolutions  of  Venus  plus  160  days,  or 
putting  this  same  result  in  the  Maya  form,  10.  o.  15.  8.  0.=  1 1.  o.  o. 
revolutions  of  the  earth  around  the  sun  plus  160  days,  or  6.  15.  15. 
synodical  revolutions  of  Venus  plus  160  days,  as  we  found  before. 


10.  19. 

8.0. 

4. 17. 

6.0.= 

6.     2. 

2.  0. 

4.  17- 

6.0.= 

I.    4. 

14.  0. 

I.    4. 

6.0.=^ 

;2- 


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